// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
// Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>
// Copyright (C) 2013 Pavel Holoborodko <pavel@holoborodko.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/*****************************************************************************
*** Platform checks for aligned malloc functions                           ***
*****************************************************************************/

#ifndef EIGEN_MEMORY_H
#define EIGEN_MEMORY_H

#ifndef EIGEN_MALLOC_ALREADY_ALIGNED

// Try to determine automatically if malloc is already aligned.

// On 64-bit systems, glibc's malloc returns 16-byte-aligned pointers, see:
//   http://www.gnu.org/s/libc/manual/html_node/Aligned-Memory-Blocks.html
// This is true at least since glibc 2.8.
// This leaves the question how to detect 64-bit. According to this document,
//   http://gcc.fyxm.net/summit/2003/Porting%20to%2064%20bit.pdf
// page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
// quite safe, at least within the context of glibc, to equate 64-bit with LP64.
#if defined(__GLIBC__) && ((__GLIBC__ >= 2 && __GLIBC_MINOR__ >= 8) || __GLIBC__ > 2) && defined(__LP64__) && !defined(__SANITIZE_ADDRESS__) && \
    (EIGEN_DEFAULT_ALIGN_BYTES == 16)
#define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
#endif

// FreeBSD 6 seems to have 16-byte aligned malloc
//   See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
// FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
//   See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
#if defined(__FreeBSD__) && !(EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
#define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
#endif

#if (EIGEN_OS_MAC && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) || (EIGEN_OS_WIN64 && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) || EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED || \
    EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
#define EIGEN_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_MALLOC_ALREADY_ALIGNED 0
#endif

#endif

namespace Eigen {

namespace internal {

    EIGEN_DEVICE_FUNC
    inline void throw_std_bad_alloc()
    {
#ifdef EIGEN_EXCEPTIONS
        throw std::bad_alloc();
#else
        std::size_t huge = static_cast<std::size_t>(-1);
#if defined(EIGEN_HIPCC)
        //
        // calls to "::operator new" are to be treated as opaque function calls (i.e no inlining),
        // and as a consequence the code in the #else block triggers the hipcc warning :
        // "no overloaded function has restriction specifiers that are compatible with the ambient context"
        //
        // "throw_std_bad_alloc" has the EIGEN_DEVICE_FUNC attribute, so it seems that hipcc expects
        // the same on "operator new"
        // Reverting code back to the old version in this #if block for the hipcc compiler
        //
        new int[huge];
#else
        void* unused = ::operator new(huge);
        EIGEN_UNUSED_VARIABLE(unused);
#endif
#endif
    }

    /*****************************************************************************
*** Implementation of handmade aligned functions                           ***
*****************************************************************************/

    /* ----- Hand made implementations of aligned malloc/free and realloc ----- */

    /** \internal Like malloc, but the returned pointer is guaranteed to be 16-byte aligned.
  * Fast, but wastes 16 additional bytes of memory. Does not throw any exception.
  */
    EIGEN_DEVICE_FUNC inline void* handmade_aligned_malloc(std::size_t size, std::size_t alignment = EIGEN_DEFAULT_ALIGN_BYTES)
    {
        eigen_assert(alignment >= sizeof(void*) && (alignment & (alignment - 1)) == 0 && "Alignment must be at least sizeof(void*) and a power of 2");

        EIGEN_USING_STD(malloc)
        void* original = malloc(size + alignment);

        if (original == 0)
            return 0;
        void* aligned = reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(alignment - 1))) + alignment);
        *(reinterpret_cast<void**>(aligned) - 1) = original;
        return aligned;
    }

    /** \internal Frees memory allocated with handmade_aligned_malloc */
    EIGEN_DEVICE_FUNC inline void handmade_aligned_free(void* ptr)
    {
        if (ptr)
        {
            EIGEN_USING_STD(free)
            free(*(reinterpret_cast<void**>(ptr) - 1));
        }
    }

    /** \internal
  * \brief Reallocates aligned memory.
  * Since we know that our handmade version is based on std::malloc
  * we can use std::realloc to implement efficient reallocation.
  */
    inline void* handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
    {
        if (ptr == 0)
            return handmade_aligned_malloc(size);
        void* original = *(reinterpret_cast<void**>(ptr) - 1);
        std::ptrdiff_t previous_offset = static_cast<char*>(ptr) - static_cast<char*>(original);
        original = std::realloc(original, size + EIGEN_DEFAULT_ALIGN_BYTES);
        if (original == 0)
            return 0;
        void* aligned =
            reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES - 1))) + EIGEN_DEFAULT_ALIGN_BYTES);
        void* previous_aligned = static_cast<char*>(original) + previous_offset;
        if (aligned != previous_aligned)
            std::memmove(aligned, previous_aligned, size);

        *(reinterpret_cast<void**>(aligned) - 1) = original;
        return aligned;
    }

    /*****************************************************************************
*** Implementation of portable aligned versions of malloc/free/realloc     ***
*****************************************************************************/

#ifdef EIGEN_NO_MALLOC
    EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed() { eigen_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)"); }
#elif defined EIGEN_RUNTIME_NO_MALLOC
    EIGEN_DEVICE_FUNC inline bool is_malloc_allowed_impl(bool update, bool new_value = false)
    {
        static bool value = true;
        if (update == 1)
            value = new_value;
        return value;
    }
    EIGEN_DEVICE_FUNC inline bool is_malloc_allowed() { return is_malloc_allowed_impl(false); }
    EIGEN_DEVICE_FUNC inline bool set_is_malloc_allowed(bool new_value) { return is_malloc_allowed_impl(true, new_value); }
    EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed()
    {
        eigen_assert(is_malloc_allowed() && "heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and g_is_malloc_allowed is false)");
    }
#else
    EIGEN_DEVICE_FUNC inline void check_that_malloc_is_allowed() {}
#endif

    /** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 or 32 bytes alignment depending on the requirements.
  * On allocation error, the returned pointer is null, and std::bad_alloc is thrown.
  */
    EIGEN_DEVICE_FUNC inline void* aligned_malloc(std::size_t size)
    {
        check_that_malloc_is_allowed();

        void* result;
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED

        EIGEN_USING_STD(malloc)
        result = malloc(size);

#if EIGEN_DEFAULT_ALIGN_BYTES == 16
        eigen_assert(
            (size < 16 || (std::size_t(result) % 16) == 0) &&
            "System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to fallback to handmade aligned memory allocator.");
#endif
#else
        result = handmade_aligned_malloc(size);
#endif

        if (!result && size)
            throw_std_bad_alloc();

        return result;
    }

    /** \internal Frees memory allocated with aligned_malloc. */
    EIGEN_DEVICE_FUNC inline void aligned_free(void* ptr)
    {
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED

        EIGEN_USING_STD(free)
        free(ptr);

#else
        handmade_aligned_free(ptr);
#endif
    }

    /**
  * \internal
  * \brief Reallocates an aligned block of memory.
  * \throws std::bad_alloc on allocation failure
  */
    inline void* aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)
    {
        EIGEN_UNUSED_VARIABLE(old_size)

        void* result;
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED
        result = std::realloc(ptr, new_size);
#else
        result = handmade_aligned_realloc(ptr, new_size, old_size);
#endif

        if (!result && new_size)
            throw_std_bad_alloc();

        return result;
    }

    /*****************************************************************************
*** Implementation of conditionally aligned functions                      ***
*****************************************************************************/

    /** \internal Allocates \a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.
  * On allocation error, the returned pointer is null, and a std::bad_alloc is thrown.
  */
    template <bool Align> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc(std::size_t size) { return aligned_malloc(size); }

    template <> EIGEN_DEVICE_FUNC inline void* conditional_aligned_malloc<false>(std::size_t size)
    {
        check_that_malloc_is_allowed();

        EIGEN_USING_STD(malloc)
        void* result = malloc(size);

        if (!result && size)
            throw_std_bad_alloc();
        return result;
    }

    /** \internal Frees memory allocated with conditional_aligned_malloc */
    template <bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_free(void* ptr) { aligned_free(ptr); }

    template <> EIGEN_DEVICE_FUNC inline void conditional_aligned_free<false>(void* ptr)
    {
        EIGEN_USING_STD(free)
        free(ptr);
    }

    template <bool Align> inline void* conditional_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)
    {
        return aligned_realloc(ptr, new_size, old_size);
    }

    template <> inline void* conditional_aligned_realloc<false>(void* ptr, std::size_t new_size, std::size_t) { return std::realloc(ptr, new_size); }

    /*****************************************************************************
*** Construction/destruction of array elements                             ***
*****************************************************************************/

    /** \internal Destructs the elements of an array.
  * The \a size parameters tells on how many objects to call the destructor of T.
  */
    template <typename T> EIGEN_DEVICE_FUNC inline void destruct_elements_of_array(T* ptr, std::size_t size)
    {
        // always destruct an array starting from the end.
        if (ptr)
            while (size) ptr[--size].~T();
    }

    /** \internal Constructs the elements of an array.
  * The \a size parameter tells on how many objects to call the constructor of T.
  */
    template <typename T> EIGEN_DEVICE_FUNC inline T* construct_elements_of_array(T* ptr, std::size_t size)
    {
        std::size_t i;
        EIGEN_TRY
        {
            for (i = 0; i < size; ++i) ::new (ptr + i) T;
            return ptr;
        }
        EIGEN_CATCH(...)
        {
            destruct_elements_of_array(ptr, i);
            EIGEN_THROW;
        }
        return NULL;
    }

    /*****************************************************************************
*** Implementation of aligned new/delete-like functions                    ***
*****************************************************************************/

    template <typename T> EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void check_size_for_overflow(std::size_t size)
    {
        if (size > std::size_t(-1) / sizeof(T))
            throw_std_bad_alloc();
    }

    /** \internal Allocates \a size objects of type T. The returned pointer is guaranteed to have 16 bytes alignment.
  * On allocation error, the returned pointer is undefined, but a std::bad_alloc is thrown.
  * The default constructor of T is called.
  */
    template <typename T> EIGEN_DEVICE_FUNC inline T* aligned_new(std::size_t size)
    {
        check_size_for_overflow<T>(size);
        T* result = reinterpret_cast<T*>(aligned_malloc(sizeof(T) * size));
        EIGEN_TRY { return construct_elements_of_array(result, size); }
        EIGEN_CATCH(...)
        {
            aligned_free(result);
            EIGEN_THROW;
        }
        return result;
    }

    template <typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new(std::size_t size)
    {
        check_size_for_overflow<T>(size);
        T* result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * size));
        EIGEN_TRY { return construct_elements_of_array(result, size); }
        EIGEN_CATCH(...)
        {
            conditional_aligned_free<Align>(result);
            EIGEN_THROW;
        }
        return result;
    }

    /** \internal Deletes objects constructed with aligned_new
  * The \a size parameters tells on how many objects to call the destructor of T.
  */
    template <typename T> EIGEN_DEVICE_FUNC inline void aligned_delete(T* ptr, std::size_t size)
    {
        destruct_elements_of_array<T>(ptr, size);
        Eigen::internal::aligned_free(ptr);
    }

    /** \internal Deletes objects constructed with conditional_aligned_new
  * The \a size parameters tells on how many objects to call the destructor of T.
  */
    template <typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete(T* ptr, std::size_t size)
    {
        destruct_elements_of_array<T>(ptr, size);
        conditional_aligned_free<Align>(ptr);
    }

    template <typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_realloc_new(T* pts, std::size_t new_size, std::size_t old_size)
    {
        check_size_for_overflow<T>(new_size);
        check_size_for_overflow<T>(old_size);
        if (new_size < old_size)
            destruct_elements_of_array(pts + new_size, old_size - new_size);
        T* result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T) * new_size, sizeof(T) * old_size));
        if (new_size > old_size)
        {
            EIGEN_TRY { construct_elements_of_array(result + old_size, new_size - old_size); }
            EIGEN_CATCH(...)
            {
                conditional_aligned_free<Align>(result);
                EIGEN_THROW;
            }
        }
        return result;
    }

    template <typename T, bool Align> EIGEN_DEVICE_FUNC inline T* conditional_aligned_new_auto(std::size_t size)
    {
        if (size == 0)
            return 0;  // short-cut. Also fixes Bug 884
        check_size_for_overflow<T>(size);
        T* result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * size));
        if (NumTraits<T>::RequireInitialization)
        {
            EIGEN_TRY { construct_elements_of_array(result, size); }
            EIGEN_CATCH(...)
            {
                conditional_aligned_free<Align>(result);
                EIGEN_THROW;
            }
        }
        return result;
    }

    template <typename T, bool Align> inline T* conditional_aligned_realloc_new_auto(T* pts, std::size_t new_size, std::size_t old_size)
    {
        check_size_for_overflow<T>(new_size);
        check_size_for_overflow<T>(old_size);
        if (NumTraits<T>::RequireInitialization && (new_size < old_size))
            destruct_elements_of_array(pts + new_size, old_size - new_size);
        T* result = reinterpret_cast<T*>(conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T) * new_size, sizeof(T) * old_size));
        if (NumTraits<T>::RequireInitialization && (new_size > old_size))
        {
            EIGEN_TRY { construct_elements_of_array(result + old_size, new_size - old_size); }
            EIGEN_CATCH(...)
            {
                conditional_aligned_free<Align>(result);
                EIGEN_THROW;
            }
        }
        return result;
    }

    template <typename T, bool Align> EIGEN_DEVICE_FUNC inline void conditional_aligned_delete_auto(T* ptr, std::size_t size)
    {
        if (NumTraits<T>::RequireInitialization)
            destruct_elements_of_array<T>(ptr, size);
        conditional_aligned_free<Align>(ptr);
    }

    /****************************************************************************/

    /** \internal Returns the index of the first element of the array that is well aligned with respect to the requested \a Alignment.
  *
  * \tparam Alignment requested alignment in Bytes.
  * \param array the address of the start of the array
  * \param size the size of the array
  *
  * \note If no element of the array is well aligned or the requested alignment is not a multiple of a scalar,
  * the size of the array is returned. For example with SSE, the requested alignment is typically 16-bytes. If
  * packet size for the given scalar type is 1, then everything is considered well-aligned.
  *
  * \note Otherwise, if the Alignment is larger that the scalar size, we rely on the assumptions that sizeof(Scalar) is a
  * power of 2. On the other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails for
  * example with Scalar=double on certain 32-bit platforms, see bug #79.
  *
  * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.
  * \sa first_default_aligned()
  */
    template <int Alignment, typename Scalar, typename Index> EIGEN_DEVICE_FUNC inline Index first_aligned(const Scalar* array, Index size)
    {
        const Index ScalarSize = sizeof(Scalar);
        const Index AlignmentSize = Alignment / ScalarSize;
        const Index AlignmentMask = AlignmentSize - 1;

        if (AlignmentSize <= 1)
        {
            // Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar
            // so that all elements of the array have the same alignment.
            return 0;
        }
        else if ((UIntPtr(array) & (sizeof(Scalar) - 1)) || (Alignment % ScalarSize) != 0)
        {
            // The array is not aligned to the size of a single scalar, or the requested alignment is not a multiple of the scalar size.
            // Consequently, no element of the array is well aligned.
            return size;
        }
        else
        {
            Index first = (AlignmentSize - (Index((UIntPtr(array) / sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;
            return (first < size) ? first : size;
        }
    }

    /** \internal Returns the index of the first element of the array that is well aligned with respect the largest packet requirement.
   * \sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */
    template <typename Scalar, typename Index> EIGEN_DEVICE_FUNC inline Index first_default_aligned(const Scalar* array, Index size)
    {
        typedef typename packet_traits<Scalar>::type DefaultPacketType;
        return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);
    }

    /** \internal Returns the smallest integer multiple of \a base and greater or equal to \a size
  */
    template <typename Index> inline Index first_multiple(Index size, Index base) { return ((size + base - 1) / base) * base; }

    // std::copy is much slower than memcpy, so let's introduce a smart_copy which
    // use memcpy on trivial types, i.e., on types that does not require an initialization ctor.
    template <typename T, bool UseMemcpy> struct smart_copy_helper;

    template <typename T> EIGEN_DEVICE_FUNC void smart_copy(const T* start, const T* end, T* target)
    {
        smart_copy_helper<T, !NumTraits<T>::RequireInitialization>::run(start, end, target);
    }

    template <typename T> struct smart_copy_helper<T, true>
    {
        EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
        {
            IntPtr size = IntPtr(end) - IntPtr(start);
            if (size == 0)
                return;
            eigen_internal_assert(start != 0 && end != 0 && target != 0);
            EIGEN_USING_STD(memcpy)
            memcpy(target, start, size);
        }
    };

    template <typename T> struct smart_copy_helper<T, false>
    {
        EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target) { std::copy(start, end, target); }
    };

    // intelligent memmove. falls back to std::memmove for POD types, uses std::copy otherwise.
    template <typename T, bool UseMemmove> struct smart_memmove_helper;

    template <typename T> void smart_memmove(const T* start, const T* end, T* target)
    {
        smart_memmove_helper<T, !NumTraits<T>::RequireInitialization>::run(start, end, target);
    }

    template <typename T> struct smart_memmove_helper<T, true>
    {
        static inline void run(const T* start, const T* end, T* target)
        {
            IntPtr size = IntPtr(end) - IntPtr(start);
            if (size == 0)
                return;
            eigen_internal_assert(start != 0 && end != 0 && target != 0);
            std::memmove(target, start, size);
        }
    };

    template <typename T> struct smart_memmove_helper<T, false>
    {
        static inline void run(const T* start, const T* end, T* target)
        {
            if (UIntPtr(target) < UIntPtr(start))
            {
                std::copy(start, end, target);
            }
            else
            {
                std::ptrdiff_t count = (std::ptrdiff_t(end) - std::ptrdiff_t(start)) / sizeof(T);
                std::copy_backward(start, end, target + count);
            }
        }
    };

#if EIGEN_HAS_RVALUE_REFERENCES
    template <typename T> EIGEN_DEVICE_FUNC T* smart_move(T* start, T* end, T* target) { return std::move(start, end, target); }
#else
    template <typename T> EIGEN_DEVICE_FUNC T* smart_move(T* start, T* end, T* target) { return std::copy(start, end, target); }
#endif

/*****************************************************************************
*** Implementation of runtime stack allocation (falling back to malloc)    ***
*****************************************************************************/

// you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA
// to the appropriate stack allocation function
#if !defined EIGEN_ALLOCA && !defined EIGEN_GPU_COMPILE_PHASE
#if EIGEN_OS_LINUX || EIGEN_OS_MAC || (defined alloca)
#define EIGEN_ALLOCA alloca
#elif EIGEN_COMP_MSVC
#define EIGEN_ALLOCA _alloca
#endif
#endif

// With clang -Oz -mthumb, alloca changes the stack pointer in a way that is
// not allowed in Thumb2. -DEIGEN_STACK_ALLOCATION_LIMIT=0 doesn't work because
// the compiler still emits bad code because stack allocation checks use "<=".
// TODO: Eliminate after https://bugs.llvm.org/show_bug.cgi?id=23772
// is fixed.
#if defined(__clang__) && defined(__thumb__)
#undef EIGEN_ALLOCA
#endif

    // This helper class construct the allocated memory, and takes care of destructing and freeing the handled data
    // at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.
    template <typename T> class aligned_stack_memory_handler : noncopyable
    {
    public:
        /* Creates a stack_memory_handler responsible for the buffer \a ptr of size \a size.
     * Note that \a ptr can be 0 regardless of the other parameters.
     * This constructor takes care of constructing/initializing the elements of the buffer if required by the scalar type T (see NumTraits<T>::RequireInitialization).
     * In this case, the buffer elements will also be destructed when this handler will be destructed.
     * Finally, if \a dealloc is true, then the pointer \a ptr is freed.
     **/
        EIGEN_DEVICE_FUNC
        aligned_stack_memory_handler(T* ptr, std::size_t size, bool dealloc) : m_ptr(ptr), m_size(size), m_deallocate(dealloc)
        {
            if (NumTraits<T>::RequireInitialization && m_ptr)
                Eigen::internal::construct_elements_of_array(m_ptr, size);
        }
        EIGEN_DEVICE_FUNC
        ~aligned_stack_memory_handler()
        {
            if (NumTraits<T>::RequireInitialization && m_ptr)
                Eigen::internal::destruct_elements_of_array<T>(m_ptr, m_size);
            if (m_deallocate)
                Eigen::internal::aligned_free(m_ptr);
        }

    protected:
        T* m_ptr;
        std::size_t m_size;
        bool m_deallocate;
    };

#ifdef EIGEN_ALLOCA

    template <typename Xpr, int NbEvaluations, bool MapExternalBuffer = nested_eval<Xpr, NbEvaluations>::Evaluate&& Xpr::MaxSizeAtCompileTime == Dynamic>
    struct local_nested_eval_wrapper
    {
        static const bool NeedExternalBuffer = false;
        typedef typename Xpr::Scalar Scalar;
        typedef typename nested_eval<Xpr, NbEvaluations>::type ObjectType;
        ObjectType object;

        EIGEN_DEVICE_FUNC
        local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr) : object(xpr)
        {
            EIGEN_UNUSED_VARIABLE(ptr);
            eigen_internal_assert(ptr == 0);
        }
    };

    template <typename Xpr, int NbEvaluations> struct local_nested_eval_wrapper<Xpr, NbEvaluations, true>
    {
        static const bool NeedExternalBuffer = true;
        typedef typename Xpr::Scalar Scalar;
        typedef typename plain_object_eval<Xpr>::type PlainObject;
        typedef Map<PlainObject, EIGEN_DEFAULT_ALIGN_BYTES> ObjectType;
        ObjectType object;

        EIGEN_DEVICE_FUNC
        local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr)
            : object(ptr == 0 ? reinterpret_cast<Scalar*>(Eigen::internal::aligned_malloc(sizeof(Scalar) * xpr.size())) : ptr, xpr.rows(), xpr.cols()),
              m_deallocate(ptr == 0)
        {
            if (NumTraits<Scalar>::RequireInitialization && object.data())
                Eigen::internal::construct_elements_of_array(object.data(), object.size());
            object = xpr;
        }

        EIGEN_DEVICE_FUNC
        ~local_nested_eval_wrapper()
        {
            if (NumTraits<Scalar>::RequireInitialization && object.data())
                Eigen::internal::destruct_elements_of_array(object.data(), object.size());
            if (m_deallocate)
                Eigen::internal::aligned_free(object.data());
        }

    private:
        bool m_deallocate;
    };

#endif  // EIGEN_ALLOCA

    template <typename T> class scoped_array : noncopyable
    {
        T* m_ptr;

    public:
        explicit scoped_array(std::ptrdiff_t size) { m_ptr = new T[size]; }
        ~scoped_array() { delete[] m_ptr; }
        T& operator[](std::ptrdiff_t i) { return m_ptr[i]; }
        const T& operator[](std::ptrdiff_t i) const { return m_ptr[i]; }
        T*& ptr() { return m_ptr; }
        const T* ptr() const { return m_ptr; }
        operator const T*() const { return m_ptr; }
    };

    template <typename T> void swap(scoped_array<T>& a, scoped_array<T>& b) { std::swap(a.ptr(), b.ptr()); }

}  // end namespace internal

/** \internal
  *
  * The macro ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) declares, allocates,
  * and construct an aligned buffer named NAME of SIZE elements of type TYPE on the stack
  * if the size in bytes is smaller than EIGEN_STACK_ALLOCATION_LIMIT, and if stack allocation is supported by the platform
  * (currently, this is Linux, OSX and Visual Studio only). Otherwise the memory is allocated on the heap.
  * The allocated buffer is automatically deleted when exiting the scope of this declaration.
  * If BUFFER is non null, then the declared variable is simply an alias for BUFFER, and no allocation/deletion occurs.
  * Here is an example:
  * \code
  * {
  *   ei_declare_aligned_stack_constructed_variable(float,data,size,0);
  *   // use data[0] to data[size-1]
  * }
  * \endcode
  * The underlying stack allocation function can controlled with the EIGEN_ALLOCA preprocessor token.
  *
  * The macro ei_declare_local_nested_eval(XPR_T,XPR,N,NAME) is analogue to
  * \code
  *   typename internal::nested_eval<XPRT_T,N>::type NAME(XPR);
  * \endcode
  * with the advantage of using aligned stack allocation even if the maximal size of XPR at compile time is unknown.
  * This is accomplished through alloca if this later is supported and if the required number of bytes
  * is below EIGEN_STACK_ALLOCATION_LIMIT.
  */
#ifdef EIGEN_ALLOCA

#if EIGEN_DEFAULT_ALIGN_BYTES > 0
// We always manually re-align the result of EIGEN_ALLOCA.
// If alloca is already aligned, the compiler should be smart enough to optimize away the re-alignment.
#define EIGEN_ALIGNED_ALLOCA(SIZE)                                                                                                    \
    reinterpret_cast<void*>((internal::UIntPtr(EIGEN_ALLOCA(SIZE + EIGEN_DEFAULT_ALIGN_BYTES - 1)) + EIGEN_DEFAULT_ALIGN_BYTES - 1) & \
                            ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES - 1)))
#else
#define EIGEN_ALIGNED_ALLOCA(SIZE) EIGEN_ALLOCA(SIZE)
#endif

#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)                                                                             \
    Eigen::internal::check_size_for_overflow<TYPE>(SIZE);                                                                                                   \
    TYPE* NAME = (BUFFER) != 0 ?                                                                                                                            \
                     (BUFFER) :                                                                                                                             \
                     reinterpret_cast<TYPE*>((sizeof(TYPE) * SIZE <= EIGEN_STACK_ALLOCATION_LIMIT) ? EIGEN_ALIGNED_ALLOCA(sizeof(TYPE) * SIZE) :            \
                                                                                                     Eigen::internal::aligned_malloc(sizeof(TYPE) * SIZE)); \
    Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME, _stack_memory_destructor)(                                                          \
        (BUFFER) == 0 ? NAME : 0, SIZE, sizeof(TYPE) * SIZE > EIGEN_STACK_ALLOCATION_LIMIT)

#define ei_declare_local_nested_eval(XPR_T, XPR, N, NAME)                                                                             \
    Eigen::internal::local_nested_eval_wrapper<XPR_T, N> EIGEN_CAT(NAME, _wrapper)(                                                   \
        XPR,                                                                                                                          \
        reinterpret_cast<typename XPR_T::Scalar*>(((Eigen::internal::local_nested_eval_wrapper<XPR_T, N>::NeedExternalBuffer) &&      \
                                                   ((sizeof(typename XPR_T::Scalar) * XPR.size()) <= EIGEN_STACK_ALLOCATION_LIMIT)) ? \
                                                      EIGEN_ALIGNED_ALLOCA(sizeof(typename XPR_T::Scalar) * XPR.size()) :             \
                                                      0));                                                                            \
    typename Eigen::internal::local_nested_eval_wrapper<XPR_T, N>::ObjectType NAME(EIGEN_CAT(NAME, _wrapper).object)

#else

#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)                                          \
    Eigen::internal::check_size_for_overflow<TYPE>(SIZE);                                                                \
    TYPE* NAME = (BUFFER) != 0 ? BUFFER : reinterpret_cast<TYPE*>(Eigen::internal::aligned_malloc(sizeof(TYPE) * SIZE)); \
    Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME, _stack_memory_destructor)((BUFFER) == 0 ? NAME : 0, SIZE, true)

#define ei_declare_local_nested_eval(XPR_T, XPR, N, NAME) typename Eigen::internal::nested_eval<XPR_T, N>::type NAME(XPR)

#endif

/*****************************************************************************
*** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF]                ***
*****************************************************************************/

#if EIGEN_HAS_CXX17_OVERALIGN

// C++17 -> no need to bother about alignment anymore :)

#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Size)

#else

// HIP does not support new/delete on device.
#if EIGEN_MAX_ALIGN_BYTES != 0 && !defined(EIGEN_HIP_DEVICE_COMPILE)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)                                 \
    EIGEN_DEVICE_FUNC                                                                         \
    void* operator new(std::size_t size, const std::nothrow_t&) EIGEN_NO_THROW                \
    {                                                                                         \
        EIGEN_TRY { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); } \
        EIGEN_CATCH(...) { return 0; }                                                        \
    }
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)                                                                                     \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void* operator new(std::size_t size) { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); }                         \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void* operator new[](std::size_t size) { return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size); }                       \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete(void* ptr)EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); }                          \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete[](void* ptr) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); }                       \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete(void* ptr, std::size_t /* sz */)EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); }    \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete[](void* ptr, std::size_t /* sz */) EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); } \
    /* in-place new and delete. since (at least afaik) there is no actual   */                                                               \
    /* memory allocated we can safely let the default implementation handle */                                                               \
    /* this particular case. */                                                                                                              \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    static void* operator new(std::size_t size, void* ptr) { return ::operator new(size, ptr); }                                             \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    static void* operator new[](std::size_t size, void* ptr) { return ::operator new[](size, ptr); }                                         \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete(void* memory, void* ptr)EIGEN_NO_THROW { return ::operator delete(memory, ptr); }                                   \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete[](void* memory, void* ptr) EIGEN_NO_THROW { return ::operator delete[](memory, ptr); }                              \
    /* nothrow-new (returns zero instead of std::bad_alloc) */                                                                               \
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)                                                                                    \
    EIGEN_DEVICE_FUNC                                                                                                                        \
    void operator delete(void* ptr, const std::nothrow_t&)EIGEN_NO_THROW { Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr); }   \
    typedef void eigen_aligned_operator_new_marker_type;
#else
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
#endif

#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Size)                                                                 \
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(                                                                                                          \
        bool(((Size) != Eigen::Dynamic) && (((EIGEN_MAX_ALIGN_BYTES >= 16) && ((sizeof(Scalar) * (Size)) % (EIGEN_MAX_ALIGN_BYTES) == 0)) ||     \
                                            ((EIGEN_MAX_ALIGN_BYTES >= 32) && ((sizeof(Scalar) * (Size)) % (EIGEN_MAX_ALIGN_BYTES / 2) == 0)) || \
                                            ((EIGEN_MAX_ALIGN_BYTES >= 64) && ((sizeof(Scalar) * (Size)) % (EIGEN_MAX_ALIGN_BYTES / 4) == 0)))))

#endif

/****************************************************************************/

/** \class aligned_allocator
* \ingroup Core_Module
*
* \brief STL compatible allocator to use with types requiring a non standrad alignment.
*
* The memory is aligned as for dynamically aligned matrix/array types such as MatrixXd.
* By default, it will thus provide at least 16 bytes alignment and more in following cases:
*  - 32 bytes alignment if AVX is enabled.
*  - 64 bytes alignment if AVX512 is enabled.
*
* This can be controlled using the \c EIGEN_MAX_ALIGN_BYTES macro as documented
* \link TopicPreprocessorDirectivesPerformance there \endlink.
*
* Example:
* \code
* // Matrix4f requires 16 bytes alignment:
* std::map< int, Matrix4f, std::less<int>,
*           aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;
* // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
* std::map< int, Vector3f > my_map_vec3;
* \endcode
*
* \sa \blank \ref TopicStlContainers.
*/
template <class T> class aligned_allocator : public std::allocator<T>
{
public:
    typedef std::size_t size_type;
    typedef std::ptrdiff_t difference_type;
    typedef T* pointer;
    typedef const T* const_pointer;
    typedef T& reference;
    typedef const T& const_reference;
    typedef T value_type;

    template <class U> struct rebind
    {
        typedef aligned_allocator<U> other;
    };

    aligned_allocator() : std::allocator<T>() {}

    aligned_allocator(const aligned_allocator& other) : std::allocator<T>(other) {}

    template <class U> aligned_allocator(const aligned_allocator<U>& other) : std::allocator<T>(other) {}

    ~aligned_allocator() {}

#if EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_LEAST(7, 0)
    // In gcc std::allocator::max_size() is bugged making gcc triggers a warning:
    // eigen/Eigen/src/Core/util/Memory.h:189:12: warning: argument 1 value '18446744073709551612' exceeds maximum object size 9223372036854775807
    // See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87544
    size_type max_size() const { return (std::numeric_limits<std::ptrdiff_t>::max)() / sizeof(T); }
#endif

    pointer allocate(size_type num, const void* /*hint*/ = 0)
    {
        internal::check_size_for_overflow<T>(num);
        return static_cast<pointer>(internal::aligned_malloc(num * sizeof(T)));
    }

    void deallocate(pointer p, size_type /*num*/) { internal::aligned_free(p); }
};

//---------- Cache sizes ----------

#if !defined(EIGEN_NO_CPUID)
#if EIGEN_COMP_GNUC && EIGEN_ARCH_i386_OR_x86_64
#if defined(__PIC__) && EIGEN_ARCH_i386
// Case for x86 with PIC
#define EIGEN_CPUID(abcd, func, id) \
    __asm__ __volatile__("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1" : "=a"(abcd[0]), "=&r"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) : "a"(func), "c"(id));
#elif defined(__PIC__) && EIGEN_ARCH_x86_64
// Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with the default small code model.
// However, we cannot detect which code model is used, and the xchg overhead is negligible anyway.
#define EIGEN_CPUID(abcd, func, id)                                                    \
    __asm__ __volatile__("xchg{q}\t{%%}rbx, %q1; cpuid; xchg{q}\t{%%}rbx, %q1"         \
                         : "=a"(abcd[0]), "=&r"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) \
                         : "0"(func), "2"(id));
#else
// Case for x86_64 or x86 w/o PIC
#define EIGEN_CPUID(abcd, func, id) __asm__ __volatile__("cpuid" : "=a"(abcd[0]), "=b"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) : "0"(func), "2"(id));
#endif
#elif EIGEN_COMP_MSVC
#if (EIGEN_COMP_MSVC > 1500) && EIGEN_ARCH_i386_OR_x86_64
#define EIGEN_CPUID(abcd, func, id) __cpuidex((int*)abcd, func, id)
#endif
#endif
#endif

namespace internal {

#ifdef EIGEN_CPUID

    inline bool cpuid_is_vendor(int abcd[4], const int vendor[3]) { return abcd[1] == vendor[0] && abcd[3] == vendor[1] && abcd[2] == vendor[2]; }

    inline void queryCacheSizes_intel_direct(int& l1, int& l2, int& l3)
    {
        int abcd[4];
        l1 = l2 = l3 = 0;
        int cache_id = 0;
        int cache_type = 0;
        do
        {
            abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
            EIGEN_CPUID(abcd, 0x4, cache_id);
            cache_type = (abcd[0] & 0x0F) >> 0;
            if (cache_type == 1 || cache_type == 3)  // data or unified cache
            {
                int cache_level = (abcd[0] & 0xE0) >> 5;        // A[7:5]
                int ways = (abcd[1] & 0xFFC00000) >> 22;        // B[31:22]
                int partitions = (abcd[1] & 0x003FF000) >> 12;  // B[21:12]
                int line_size = (abcd[1] & 0x00000FFF) >> 0;    // B[11:0]
                int sets = (abcd[2]);                           // C[31:0]

                int cache_size = (ways + 1) * (partitions + 1) * (line_size + 1) * (sets + 1);

                switch (cache_level)
                {
                case 1:
                    l1 = cache_size;
                    break;
                case 2:
                    l2 = cache_size;
                    break;
                case 3:
                    l3 = cache_size;
                    break;
                default:
                    break;
                }
            }
            cache_id++;
        } while (cache_type > 0 && cache_id < 16);
    }

    inline void queryCacheSizes_intel_codes(int& l1, int& l2, int& l3)
    {
        int abcd[4];
        abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
        l1 = l2 = l3 = 0;
        EIGEN_CPUID(abcd, 0x00000002, 0);
        unsigned char* bytes = reinterpret_cast<unsigned char*>(abcd) + 2;
        bool check_for_p2_core2 = false;
        for (int i = 0; i < 14; ++i)
        {
            switch (bytes[i])
            {
            case 0x0A:
                l1 = 8;
                break;  // 0Ah   data L1 cache, 8 KB, 2 ways, 32 byte lines
            case 0x0C:
                l1 = 16;
                break;  // 0Ch   data L1 cache, 16 KB, 4 ways, 32 byte lines
            case 0x0E:
                l1 = 24;
                break;  // 0Eh   data L1 cache, 24 KB, 6 ways, 64 byte lines
            case 0x10:
                l1 = 16;
                break;  // 10h   data L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
            case 0x15:
                l1 = 16;
                break;  // 15h   code L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
            case 0x2C:
                l1 = 32;
                break;  // 2Ch   data L1 cache, 32 KB, 8 ways, 64 byte lines
            case 0x30:
                l1 = 32;
                break;  // 30h   code L1 cache, 32 KB, 8 ways, 64 byte lines
            case 0x60:
                l1 = 16;
                break;  // 60h   data L1 cache, 16 KB, 8 ways, 64 byte lines, sectored
            case 0x66:
                l1 = 8;
                break;  // 66h   data L1 cache, 8 KB, 4 ways, 64 byte lines, sectored
            case 0x67:
                l1 = 16;
                break;  // 67h   data L1 cache, 16 KB, 4 ways, 64 byte lines, sectored
            case 0x68:
                l1 = 32;
                break;  // 68h   data L1 cache, 32 KB, 4 ways, 64 byte lines, sectored
            case 0x1A:
                l2 = 96;
                break;  // code and data L2 cache, 96 KB, 6 ways, 64 byte lines (IA-64)
            case 0x22:
                l3 = 512;
                break;  // code and data L3 cache, 512 KB, 4 ways (!), 64 byte lines, dual-sectored
            case 0x23:
                l3 = 1024;
                break;  // code and data L3 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x25:
                l3 = 2048;
                break;  // code and data L3 cache, 2048 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x29:
                l3 = 4096;
                break;  // code and data L3 cache, 4096 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x39:
                l2 = 128;
                break;  // code and data L2 cache, 128 KB, 4 ways, 64 byte lines, sectored
            case 0x3A:
                l2 = 192;
                break;  // code and data L2 cache, 192 KB, 6 ways, 64 byte lines, sectored
            case 0x3B:
                l2 = 128;
                break;  // code and data L2 cache, 128 KB, 2 ways, 64 byte lines, sectored
            case 0x3C:
                l2 = 256;
                break;  // code and data L2 cache, 256 KB, 4 ways, 64 byte lines, sectored
            case 0x3D:
                l2 = 384;
                break;  // code and data L2 cache, 384 KB, 6 ways, 64 byte lines, sectored
            case 0x3E:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 4 ways, 64 byte lines, sectored
            case 0x40:
                l2 = 0;
                break;  // no integrated L2 cache (P6 core) or L3 cache (P4 core)
            case 0x41:
                l2 = 128;
                break;  // code and data L2 cache, 128 KB, 4 ways, 32 byte lines
            case 0x42:
                l2 = 256;
                break;  // code and data L2 cache, 256 KB, 4 ways, 32 byte lines
            case 0x43:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 4 ways, 32 byte lines
            case 0x44:
                l2 = 1024;
                break;  // code and data L2 cache, 1024 KB, 4 ways, 32 byte lines
            case 0x45:
                l2 = 2048;
                break;  // code and data L2 cache, 2048 KB, 4 ways, 32 byte lines
            case 0x46:
                l3 = 4096;
                break;  // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines
            case 0x47:
                l3 = 8192;
                break;  // code and data L3 cache, 8192 KB, 8 ways, 64 byte lines
            case 0x48:
                l2 = 3072;
                break;  // code and data L2 cache, 3072 KB, 12 ways, 64 byte lines
            case 0x49:
                if (l2 != 0)
                    l3 = 4096;
                else
                {
                    check_for_p2_core2 = true;
                    l3 = l2 = 4096;
                }
                break;  // code and data L3 cache, 4096 KB, 16 ways, 64 byte lines (P4) or L2 for core2
            case 0x4A:
                l3 = 6144;
                break;  // code and data L3 cache, 6144 KB, 12 ways, 64 byte lines
            case 0x4B:
                l3 = 8192;
                break;  // code and data L3 cache, 8192 KB, 16 ways, 64 byte lines
            case 0x4C:
                l3 = 12288;
                break;  // code and data L3 cache, 12288 KB, 12 ways, 64 byte lines
            case 0x4D:
                l3 = 16384;
                break;  // code and data L3 cache, 16384 KB, 16 ways, 64 byte lines
            case 0x4E:
                l2 = 6144;
                break;  // code and data L2 cache, 6144 KB, 24 ways, 64 byte lines
            case 0x78:
                l2 = 1024;
                break;  // code and data L2 cache, 1024 KB, 4 ways, 64 byte lines
            case 0x79:
                l2 = 128;
                break;  // code and data L2 cache, 128 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x7A:
                l2 = 256;
                break;  // code and data L2 cache, 256 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x7B:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x7C:
                l2 = 1024;
                break;  // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
            case 0x7D:
                l2 = 2048;
                break;  // code and data L2 cache, 2048 KB, 8 ways, 64 byte lines
            case 0x7E:
                l2 = 256;
                break;  // code and data L2 cache, 256 KB, 8 ways, 128 byte lines, sect. (IA-64)
            case 0x7F:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 2 ways, 64 byte lines
            case 0x80:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 8 ways, 64 byte lines
            case 0x81:
                l2 = 128;
                break;  // code and data L2 cache, 128 KB, 8 ways, 32 byte lines
            case 0x82:
                l2 = 256;
                break;  // code and data L2 cache, 256 KB, 8 ways, 32 byte lines
            case 0x83:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 8 ways, 32 byte lines
            case 0x84:
                l2 = 1024;
                break;  // code and data L2 cache, 1024 KB, 8 ways, 32 byte lines
            case 0x85:
                l2 = 2048;
                break;  // code and data L2 cache, 2048 KB, 8 ways, 32 byte lines
            case 0x86:
                l2 = 512;
                break;  // code and data L2 cache, 512 KB, 4 ways, 64 byte lines
            case 0x87:
                l2 = 1024;
                break;  // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines
            case 0x88:
                l3 = 2048;
                break;  // code and data L3 cache, 2048 KB, 4 ways, 64 byte lines (IA-64)
            case 0x89:
                l3 = 4096;
                break;  // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines (IA-64)
            case 0x8A:
                l3 = 8192;
                break;  // code and data L3 cache, 8192 KB, 4 ways, 64 byte lines (IA-64)
            case 0x8D:
                l3 = 3072;
                break;  // code and data L3 cache, 3072 KB, 12 ways, 128 byte lines (IA-64)

            default:
                break;
            }
        }
        if (check_for_p2_core2 && l2 == l3)
            l3 = 0;
        l1 *= 1024;
        l2 *= 1024;
        l3 *= 1024;
    }

    inline void queryCacheSizes_intel(int& l1, int& l2, int& l3, int max_std_funcs)
    {
        if (max_std_funcs >= 4)
            queryCacheSizes_intel_direct(l1, l2, l3);
        else if (max_std_funcs >= 2)
            queryCacheSizes_intel_codes(l1, l2, l3);
        else
            l1 = l2 = l3 = 0;
    }

    inline void queryCacheSizes_amd(int& l1, int& l2, int& l3)
    {
        int abcd[4];
        abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;

        // First query the max supported function.
        EIGEN_CPUID(abcd, 0x80000000, 0);
        if (static_cast<numext::uint32_t>(abcd[0]) >= static_cast<numext::uint32_t>(0x80000006))
        {
            EIGEN_CPUID(abcd, 0x80000005, 0);
            l1 = (abcd[2] >> 24) * 1024;  // C[31:24] = L1 size in KB
            abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
            EIGEN_CPUID(abcd, 0x80000006, 0);
            l2 = (abcd[2] >> 16) * 1024;                      // C[31;16] = l2 cache size in KB
            l3 = ((abcd[3] & 0xFFFC000) >> 18) * 512 * 1024;  // D[31;18] = l3 cache size in 512KB
        }
        else
        {
            l1 = l2 = l3 = 0;
        }
    }
#endif

    /** \internal
 * Queries and returns the cache sizes in Bytes of the L1, L2, and L3 data caches respectively */
    inline void queryCacheSizes(int& l1, int& l2, int& l3)
    {
#ifdef EIGEN_CPUID
        int abcd[4];
        const int GenuineIntel[] = {0x756e6547, 0x49656e69, 0x6c65746e};
        const int AuthenticAMD[] = {0x68747541, 0x69746e65, 0x444d4163};
        const int AMDisbetter_[] = {0x69444d41, 0x74656273, 0x21726574};  // "AMDisbetter!"

        // identify the CPU vendor
        EIGEN_CPUID(abcd, 0x0, 0);
        int max_std_funcs = abcd[0];
        if (cpuid_is_vendor(abcd, GenuineIntel))
            queryCacheSizes_intel(l1, l2, l3, max_std_funcs);
        else if (cpuid_is_vendor(abcd, AuthenticAMD) || cpuid_is_vendor(abcd, AMDisbetter_))
            queryCacheSizes_amd(l1, l2, l3);
        else
            // by default let's use Intel's API
            queryCacheSizes_intel(l1, l2, l3, max_std_funcs);

            // here is the list of other vendors:
            //   ||cpuid_is_vendor(abcd,"VIA VIA VIA ")
            //   ||cpuid_is_vendor(abcd,"CyrixInstead")
            //   ||cpuid_is_vendor(abcd,"CentaurHauls")
            //   ||cpuid_is_vendor(abcd,"GenuineTMx86")
            //   ||cpuid_is_vendor(abcd,"TransmetaCPU")
            //   ||cpuid_is_vendor(abcd,"RiseRiseRise")
            //   ||cpuid_is_vendor(abcd,"Geode by NSC")
            //   ||cpuid_is_vendor(abcd,"SiS SiS SiS ")
            //   ||cpuid_is_vendor(abcd,"UMC UMC UMC ")
            //   ||cpuid_is_vendor(abcd,"NexGenDriven")
#else
        l1 = l2 = l3 = -1;
#endif
    }

    /** \internal
 * \returns the size in Bytes of the L1 data cache */
    inline int queryL1CacheSize()
    {
        int l1(-1), l2, l3;
        queryCacheSizes(l1, l2, l3);
        return l1;
    }

    /** \internal
 * \returns the size in Bytes of the L2 or L3 cache if this later is present */
    inline int queryTopLevelCacheSize()
    {
        int l1, l2(-1), l3(-1);
        queryCacheSizes(l1, l2, l3);
        return (std::max)(l2, l3);
    }

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_MEMORY_H
